Maximum Measurable Velocity in Frequency Modulated Continuous Wave (FMCW) Radar

ABSTRACT

A radar system is provided that includes a radar transceiver integrated circuit (IC) configurable to transmit a first frame of chirps, and another radar transceiver IC configurable to transmit a second frame of chirps at a time delay ΔT, wherein ΔT=T c /K, K≥2 and T c  is an elapsed time from a start of one chirp in the first frame and the second frame and a start of a next chirp in the first frame and the second frame, wherein the radar system is configured to determine a velocity of an object in a field of view of the radar system based on first digital intermediate frequency signals generated responsive to receiving reflected chirps of the first frame and second digital IF signals generated responsive to receiving reflected chirps of the time delayed second frame, wherein the maximum measurable velocity is increased by a factor of K.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of India Provisional Patent ApplicationSerial No. 201641042728, filed Dec. 15, 2016, which is incorporatedherein by reference in its entirety.

BACKGROUND OF THE DISCLOSURE Field of the Disclosure

Embodiments of the present disclosure generally relate to frequencymodulated continuous wave (FMCW) radar systems, and more specificallyrelate to improving the maximum measurable velocity in an FMCW radarsystem.

Description of the Related Art

The use of embedded frequency modulated continuous wave (FMCW) radarsystems in industrial and automotive applications is evolving rapidly.For example, embedded FMCW radar systems may be used in a number ofapplications associated with a vehicle such as adaptive cruise control,collision warning, blind spot warning, lane change assist, parkingassist and rear collision warning. Further, embedded FMCW radar systemsmay be used in industrial or security applications such as trackingmovement inside a house or building under surveillance and maneuvering arobot in a factory or warehouse.

An FMCW radar transmits a series of equally spaced frequency ramps, alsoreferred to as chirps, in a unit referred to as a frame. The reflectedsignal is down-converted, digitized and processed to estimate the range,velocity and angle of arrival of objects in front of the radar. Themaximum unambiguous velocity that can be measured is a key care-about insuch a radar system as the estimation of the velocity of objects movingat a velocity greater than the maximum measurable velocity may beerroneous in both magnitude and sign. For example, for a radar with amaximum measurable velocity of 70 kilometers per hour (kmph), therelative velocity of an object moving at 75 kmph may be estimated as avelocity of −5 kmph.

SUMMARY

Embodiments of the present disclosure relate to methods and apparatusfor improving the maximum measurable velocity in a frequency modulatedcontinuous wave (FMCW) radar system. In one aspect, radar system havinga maximum measurable velocity v_(max) is provided that includes a firstradar transceiver integrated circuit (IC) configurable to transmit afirst frame of chirps, and a second radar transceiver IC configurable totransmit a second frame of chirps at a time delay ΔT from when the firstradar transceiver IC begins transmitting the first frame of chirps,wherein ΔT=T_(c)/K, K≥2 and T_(c) is an elapsed time from a start of onechirp in the first frame of chirps and the second frame of chirps and astart of a next chirp in the first frame and the second frame, whereinthe radar system is configured to determine a velocity of an object in afield of view (FOV) of the radar system based on first digitalintermediate frequency (IF) signals generated by the first radartransceiver IC responsive to receiving reflected chirps of the firstframe of chirps and second digital IF signals generated by the secondradar transceiver IC responsive to receiving reflected chirps of thetime delayed second frame of chirps, wherein v_(max) is increased by afactor of K.

In one aspect, a method for determining velocity of objects in a radarsystem having a maximum measurable velocity v_(max) is provided thatincludes initiating transmission of a first frame of chirps by a firstradar transceiver integrated circuit (IC) in the radar system,initiating transmission of a second frame of chirps by a second radartransceiver IC in the radar system at a time delay ΔT from when thefirst radar transceiver IC begins transmitting the frame of chirps,wherein ΔT=T_(c)/K, K≥2 and T_(c) is an elapsed time from a start of onechirp in the first frame of chirps and the second frame and a start of anext chirp in the first frame and the second frame, generating firstdigital intermediate frequency (IF) signals by the first radartransceiver IC responsive to receiving reflected chirps of the firstframe of chirps, generating second digital IF signals by the secondradar transceiver IC responsive to receiving reflected chirps of thetime delayed second frame of chirps, and determining a velocity of anobject in a field of view (FOV) of the radar system based on the firstdigital IF signals and the second digital IF signals, wherein v_(max) isincreased by a factor of K.

BRIEF DESCRIPTION OF THE DRAWINGS

Particular embodiments will now be described, by way of example only,and with reference to the accompanying drawings:

FIGS. 1A and 1B are examples illustrated staggered chirp transmission;

FIGS. 2 and 3 are block diagrams of an example frequency modulatedcontinuous wave (FMCW) radar system;

FIGS. 4 and 6 are flow diagrams of methods for increasing the maximummeasurable velocity in a radar system;

FIG. 5 is an example illustrating interleaving of range arrays;

FIG. 7 is a flow diagram of a method for determining the velocity of anobject;

FIG. 8 is an example illustrating transmit and receive antenna routingbetween two radar transceiver integrated circuits;

FIG. 9 is an example illustrating the principle of antenna equivalence;

FIG. 10 is an example antenna configuration designed using the principleof antenna equivalence; and

FIGS. 11 and 12 are flow diagrams of methods for determining systemicphase offsets.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE DISCLOSURE

Specific embodiments of the disclosure will now be described in detailwith reference to the accompanying figures. Like elements in the variousfigures are denoted by like reference numerals for consistency.

In a typical frequency modulated continuous wave (FMCW) radar system,consecutive sequences of equally spaced chirps are transmitted andreceived to generate radar signals. After each consecutive sequence ofchirps, there is some idle time (inter-frame idle) to allow forprocessing the resulting radar signals. The acquisition time of asequence of chirps and the subsequent inter-frame idle time form a radarframe. The reflected signal from each antenna is mixed with thetransmitted signal to generate an intermediate frequency (IF) signalthat is filtered and digitized. Signal processing is then performed onthe resulting digital IF signals (one per receiving antenna in thesystem) to extract the range, velocity, and angle of potential objectsin the view of the radar.

The signal processing may be performed as follows. For each receivechannel, a range Fast Fourier Transform (FFT) is performed on thedigitized samples of each reflected chirp to convert the data to thefrequency domain. Peak values in the resulting array correspond toranges (distances) of potential objects. The results of the range FFTsare saved in memory for further processing. There will be one set ofrange FFT results, i.e., one range array, for each receive antenna. Notethat if there are N time samples in a chirp, N range results eachcorresponding to a specific range bin are stored for the chirp. Thus,logically, if there are M chirps in the chirp sequence, arrays of M×Nrange values are generated by the range FFTs. In these arrays, the Ncolumns are the signal values for the corresponding range bins acrossthe M chirps.

For each range array, a Doppler FFT is performed over each of thecorresponding range values of the chirps in the chirp sequence. That is,a Doppler FFT is performed on each of the N columns of the M×N array.The peaks in the resulting M×N range-Doppler plane, also referred to asa range-Doppler array or range-Doppler slice, correspond to the rangeand relative speed (velocity) of potential objects. There will be arange-Doppler array for each receive antenna.

Coherent integration may then be performed across the range-Dopplerarrays to determine angle information of the potential objects. Whenmultiple receivers each connected to a receive antenna are used, thereflected signals will each have a different delay depending on theangle of an object reflecting the signal. For coherent integration, athird FFT, i.e., an angle FFT, is performed across the range-Dopplerarrays for each antenna. Potential objects are detected by consideringpeaks in the range-Doppler-angle cubes. The information regarding thepotential objects may then used for application specific processing suchas object tracking, rate of movement of objects, direction of movement,etc. In the automotive context, the object data may be used, forexample, for lane change assistance, parking, blind spot detection, rearcollision alert, emergency braking, and cruise control.

As previously mentioned, the maximum unambiguous velocity v_(max) thatcan be measured is a key care-about in a frequency modulated continuouswave (FMCW) radar system. Velocity is estimated by measuring the phasedifference across consecutive received chirps. Thus, a large chirpperiodicity T_(c), i.e., the elapsed time from the start of one chirp tothe start of the next chirp, can result in a phase rollover which causeserrors in the estimated velocity. The achievable v_(max) is inverselyproportional to T_(c), i.e., is given by v_(max)=λ/(4T_(c)), where λ isthe wavelength corresponding to the starting frequency of a chirp.However, various factors limit the minimum achievable T_(c), and thuslimit the maximum measurable v_(max). These factors include thebandwidth spanned by a chirp, the slope of the chirp, and, in some FMCWradar configurations, multiple transmitters transmitting in sequence.

The bandwidth of a chirp affects range resolution, i.e., the larger thebandwidth, the better the range resolution. However, increasing thechirp bandwidth to improve range resolution increases T_(c). The maximumslope of a chirp is limited by the bandwidth of the chirp generationcircuitry, the IF bandwidth of the receive channels, and the maximumdistance supported by the radar. As chirp slope decreases, T_(c)increases for a given bandwidth spanned by the chirp. If the FMCW radarprovides a time division multiplexed multiple input multiple output(TDM-MIMO) mode of operation which improves angle resolution, multipletransmitters transmit in sequence, which increases the effective T_(c).In the context of TDM-MIMO, T_(c) is defined as the elapsed time fromthe start of one chirp to the start of the next chirp from the sametransmitter.

Embodiments of the disclosure provide for increasing the maximummeasurable v_(max) of an FMCW radar system. In some embodiments, chirpsin frames generated by two radar transceiver integrated circuits (ICs)in a radar system are transmitted such that there is a time delay ΔTbetween when one master radar transceiver IC begins transmission andwhen the other radar transceiver IC begins transmission, i.e., thetransmitted chirps from the two radar transceiver ICs are interleaved orstaggered by ΔT, where ΔT=T_(c)/K, K≥2. The staggered transmissiondecreases the effective T_(c) by a factor of K, thus improving v_(max)by a factor of K. As illustrated in FIG. 1A for two ICs, when K=2, thestaggering of the transmitted chirps is symmetrical, i.e., the spacebetween all adjacent chirps is the same. As illustrated in FIG. 1B, whenK>2, the staggering of the transmitted chirps is asymmetrical. In somesuch embodiments, the radar system is configured to switch between twomodes of operation: a mode favoring increased angle resolution and amode favoring increased v_(max).

FIGS. 2 and 3 are block diagrams of an example FMCW radar system 200configured to increase the maximum measurable velocity. FIG. 2illustrates the top level architecture of the radar system 200 and FIG.3 illustrates an example FMCW radar transceiver integrated circuit (IC)suitable for use in the radar system 200.

Referring first to FIG. 2, the example FMCW radar system 200 illustratedis suitable for use in an embedded application. The radar system 200includes a master radar transceiver integrated circuit (IC) 202, a slaveradar transceiver IC 204, and a processing unit 206. The master radartransceiver IC 202 and the slave radar transceiver IC 204 each have thearchitecture of the example FMCW radar transceiver IC of FIG. 3.Further, the master radar transceiver IC 202 is coupled to the slaveradar transceiver IC 204 to allow for synchronization of the operationof the slave radar transceiver IC 204 with that of the master radartransceiver IC 202. The master radar transceiver IC 202 and the slaveradar transceiver IC 204 may be referred to collectively herein as theradar system front end or the front end.

The processing unit 206 is coupled to the master radar transceiver IC202 and the slave radar transceiver IC 204 via a serial interface toreceive data from the radar transceiver ICs. In some embodiments, theserial interface may be a high speed serial interface such as alow-voltage differential signaling (LVDS) interface. In someembodiments, the serial interface may be lower speed serial peripheralinterface (SPI). As is explained in more detail in reference to FIG. 3,each radar transceiver IC 202, 204 includes functionality to generatemultiple digital intermediate frequency (IF) signals (alternativelyreferred to as dechirped signals, beat signals, or raw radar signals)from reflected chirps. Further, each radar transceiver IC 202, 204 mayinclude functionality to perform part of the signal processing of radarsignals received in the IC, and to provide the results of this signalprocessing to the processing unit 206 via the serial interface. In someembodiments, each radar transceiver IC 202, 204 performs the range FFTfor each radar frame. In some embodiments, each radar transceiver IC202, 204 performs the range FFT and the Doppler FFT for each radarframe.

The processing unit 206 includes functionality to process the datareceived from the radar transceiver ICs 202, 204 to complete anyremaining signal processing to determine, for example, distance,velocity, and angle of any detected objects. The processing unit 206 mayalso include functionality to perform post processing of the informationabout the detected objects, such as tracking objects, determining rateand direction of movement, etc. The processing unit 206 may performvelocity determination as per an embodiment of methods for increasingthe maximum measurable velocity described herein. The processing unit206 may include any suitable processor or combination of processors asneeded for the processing throughput of the application using the radardata. For example, the processing unit 206 may include a digital signalprocessor (DSP), a microcontroller (MCU), an SOC combining both DSP andMCU processing, or a floating point gate array (FPGA) and a DSP.

Referring now to FIG. 3, the radar transceiver IC 300 may includemultiple transmit channels 304 for transmitting FMCW signals andmultiple receive channels 302 for receiving the reflected transmittedsignals. Any suitable number of receive channels and transmit channelsmay be used in embodiments. Further, the number of receive channels andthe number of transmit channels may not be the same. For example, anembodiment of the radar transceiver IC 300 may have two transmitchannels and four receive channels.

A transmit channel 304 includes a suitable transmitter coupled to atransmit antenna. Further, each of the transmit channels 304 areidentical and include a power amplified (PA) 307, 309 coupled between atransmit antenna and the RFSYNTH 330 to amplify the transmitted signal.A receive channel 302 includes a suitable receiver coupled to a receiveantenna. Further, each of the receive channels 302 are identical andinclude a low-noise amplifier (LNA) 303, 305 to amplify the receivedradio frequency (RF) signal, a mixer 306, 308 to mix the transmitted,i.e., local oscillator (LO), signal with the received RF signal togenerate an intermediate frequency (IF) signal, a baseband bandpassfilter 310, 312 for filtering the IF signal, a variable gain amplifier(VGA) 314, 316 for amplifying the filtered IF signal, and ananalog-to-digital converter (ADC) 318, 320 for converting the analog IFsignal to a digital IF signal. The bandpass filter, VGA, and ADC of areceive channel may be collectively referred to as the analog baseband,the baseband chain, the complex baseband, or the baseband filter chain.Further, the bandpass filter and VGA may be collectively referred to asan IF amplifier (IFA).

The receive channels 302 are coupled to the digital front end (DFE)component 322 to provide the digital IF signals to the DFE 322. The DFE322, which may also be referred to as the digital baseband, may includefunctionality to perform decimation filtering on the digital IF signalsto reduce the data transfer rate. The DFE 322 may also perform otheroperations on the digital IF signals, e.g., DC offset removal, digitalcompensation of non-idealities in the receive channels, such as inter-RXgain imbalance non-ideality, inter-RX phase imbalance non-ideality andthe like. The DFE 322 is coupled to the signal processor component 344to transfer the output of the DFE 322 to the signal processor component344.

The signal processor component 344 is configured to perform a portion ofthe signal processing on the digital IF signals from a frame of chirpsand to provide the results of this signal processing to the processingunit 206. In some embodiments, the results are provided to theprocessing unit 206 via the high speed serial interface 324. In someembodiments, the results are provided via the serial peripheralinterface (SPI) 328. In some embodiments, the signal processor component344 may perform the range FFT on each sequence of chirps in a radarframe. In some embodiments, the signal processor component 344 may alsoperform the Doppler FFT on the results of the range FFTs.

The signal processor component 344 may include any suitable processor orcombination of processors. For example, the signal processor component344 may be a digital signal processor, an MCU, an FFT engine, a DSP+MCUprocessor, a field programmable gate array (FPGA), or an applicationspecific integrated circuit (ASIC). The signal processor component 344is coupled to memory 348 to store intermediate results of the portion ofthe signal processing performed on the digital IF signals.

The on-chip memory component 348 provides on-chip storage, e.g., acomputer readable medium, which may be used, for example, to communicatedata between the various components of the IC 300, to store softwareprograms executed by processors on the IC 300, etc. The on-chip memorycomponent 348 may include any suitable combination of read-only memoryand/or random access memory (RAM), e.g., static RAM. The direct memoryaccess (DMA) component 346 is coupled to the memory component 348 toperform data transfers from the memory component 348 to the high speedinterface 324 and/or the SPI 328.

The serial peripheral interface (SPI) 328 provides an interface forcommunication with the processing unit 206. For example, the processingunit 206 may use the SPI 328 to send control information, e.g., timingand frequencies of chirps, output power level, triggering of monitoringfunctions, etc., to the control module 326. The radar transceiver IC 300may use the SPI 328, for example, to send test data to the processingunit 206.

The control module 326 includes functionality to control the operationof the radar transceiver IC 300. The control module 326 may include, forexample, a microcontroller that executes firmware to control theoperation of the radar transceiver IC 300.

The programmable timing engine 342 includes functionality to receivechirp parameter values for a sequence of chirps in a radar frame fromthe control module 326 and to generate chirp control signals thatcontrol the transmission and reception of the chirps in a frame based onthe parameter values. The chirp parameters are defined by the radarsystem architecture and may include, for example, a transmitter enableparameter for indicating which transmitters to enable, a chirp frequencystart value, a chirp frequency slope, an analog-to-digital (ADC)sampling time, a ramp end time, a transmitter start time, etc.

The radio frequency synthesizer (RFSYNTH) 330 includes functionality togenerate signals for transmission based on chirp control signals fromthe timing engine 342. In some embodiments, the RFSYNTH 330 includes aphase locked loop (PLL) with a voltage controlled oscillator (VCO).

The multiplexor 332 is coupled to the RFSYNTH 330 and the input buffer336. The multiplexor 332 is configurable to select between signalsreceived in the input buffer 336 and signals generated by the RFSYNTH330. The output buffer 338 is coupled to the multiplexor 332 and may beused, for example, to transmit signals selected by the multiplexor 332to the input buffer of another radar transceiver IC. For example, theoutput buffer 338 of the master radar transceiver IC 202 is coupled tothe input buffer 336 of the slave radar transceiver IC 204 to sendsignals from the RFSYNTH 330 of the master radar transceiver IC 202 tothe slave radar transceiver IC 204. Further, the multiplexer 332 of theslave radar transceiver IC 204 is configured to select the signalsreceived in the input buffer 336.

The clock multiplier 340 increases the frequency of the transmissionsignal (LO signal) to the LO frequency of the mixers 306, 308. Theclean-up PLL (phase locked loop) 334 operates to increase the frequencyof the signal of an external low frequency reference clock (not shown)to the frequency of the RFSYNTH 330 and to filter the reference clockphase noise out of the clock signal.

FIGS. 4 and 6 are flow diagrams of methods for increasing the maximummeasurable velocity in a radar system such as that of FIGS. 2 and 3. Aspreviously mentioned, the maximum measurable velocity v_(max) of a radarsystem may be increased by staggering the transmissions of the masterradar transceiver IC and the slave radar IC by a time delay ΔT whereΔT=T_(c)/K, K≥2 and T_(c) is the chirp periodicity. The method of FIG. 4is for the symmetrical case where K=2 and the method of FIG. 6 is forthe asymmetrical case where K>2. For simplicity of explanation, themethods are described in reference to the two IC architecture of FIGS. 2and 3. Further, the method is explained assuming that each radartransceiver IC has four receive channels and two transmit channels. Oneof ordinary skill in the art will understand embodiments in which theradar transceiver ICs may have more or fewer receive channels and/ortransmit channels.

Referring first to FIG. 4, the transmission of a frame of chirps withchirp periodicity T_(c) is initiated 400 by the master radar transceiverIC 202. The transmission of a frame of chirps by the slave radartransceiver IC 204 is then initiated 402 with a time delay of T_(c)/2.As shown in FIG. 2, the master radar transceiver IC 202 and the slaveradar transceiver IC 204 are connected by a synchronization (SYNC)signal line that is used to indicate to the slave IC 204 when the masterIC 204 has started transmission. The slave IC 204 is programmed toinitiate transmission with a delay of T_(c)/2 in response to the SYNCsignal. Digital IF signals are generated 404 in each receive channel 302of each of the radar transceiver ICs 202, 204 as the reflected chirpsare received. Thus, four digital IF signals, one from each receivechannel 302, are generated in each radar transceiver IC 202, 204.

Range FFTs are performed 406 on the digital IF signals to generate arange array for each digital IF signal. That is, four M×N range arraysfrom, each from a respective one of the four receive channels 302, aregenerated in each radar transceiver IC 202, 204, where M is the numberof chirps in the chirp sequence and N is the number of time samples forreceiving a chirp. In some embodiments, respective range FFTs areperformed in the signal processor 344 of each radar transceiver IC 202,204 and the resulting range arrays are communicated to the processingunit 206. In some embodiments, the digital IF signals are communicatedto the processing unit 206, which performs the range FFTs.

The corresponding range arrays of the master radar transceiver IC 202and the range arrays of the slave radar transceiver IC 204 areinterleaved 408 row by row to generate four 2 M×N range arrays.Correspondence of receive channels is explained below herein. That is,the rows of the range array resulting from a receive channel of themaster radar transceiver IC 202 and the rows of the range arrayresulting from the corresponding receive channel of the slave radartransceiver IC 204 are interleaved to form a 2 M×N interleaved rangearray. An example of the interleaving is shown in FIG. 5. In thisexample, a small M×N array 500 and a small M×N array 502 are interleavedto create the 2 M×N interleaved range array 504. Note that the resultinginterleaved range array is equivalent to a range array that would resultfrom a single frame of chirps with an inter-chirp spacing of T/2, thusdoubling v_(max). The rows of the range arrays of the othercorresponding receive channels are similarly interleaved.

Doppler FFTs are performed 410 on each interleaved range array togenerate four range-Doppler arrays. That is, a Doppler FFT is performedon each of the N columns of each 2 M×N interleaved range array. The fourrange-Doppler arrays are then combined 412 to form a combinedrange-Doppler array. The combining may be performed, for example, bynon-coherently adding the corresponding elements of each of the fourrange-Doppler arrays. Non-coherent addition may involve performing anon-linear operation, e.g., squaring, on each of the range-Dopplerarrays, and then performing an element by element addition of theresulting arrays to create a single combined range-Doppler array. Peaksin the resulting combined range-Doppler array are potential objects andthe velocity of these potential objects may be determined 414 from thecombined range-Doppler array. More specifically, the row and columnnumber of a peak in the combined range-Doppler array respectivelycorrespond to the range and the velocity of a potential object.

Referring now to FIG. 6, the transmission of a frame of chirps withchirp period T_(c) is initiated 600 by the master radar transceiver IC202. The transmission of a frame of chirps by the slave radartransceiver IC 204 is then initiated 602 with a time delay T_(c)/K,where K>2. As shown in FIG. 2, the master radar transceiver IC 202 andthe slave radar transceiver IC 204 are connected by a synchronization(SYNC) signal line that is used to indicate to the slave IC 204 when themaster IC 204 has started transmission. The slave IC 204 is programmedto initiate transmission with a delay of T_(c)/K in response to the SYNCsignal. Digital IF signals are generated 604 in each receive channel 302of each of the radar transceiver ICs 202, 204 as the reflected chirpsare received. Thus, four digital IF signals are generated in each radartransceiver IC 202, 204.

Range FFTs are performed 606 on the digital IF signals to generate arange array for each digital IF signal. That is, four M×N range arraysare generated where M is the number of chirps in the chirp sequence andN is the number of time samples for receiving a chirp. In someembodiments, respective range FFTs are performed in the signal processor344 of each radar transceiver IC 202, 204 and the resulting range arraysare communicated to the processing unit 206. In some embodiments, thedigital IF signals are communicated to the processing unit 206, whichperforms the range FFTs.

Doppler FFTs are then performed 608 on each of the range arrays togenerate eight range-Doppler arrays. That is, a Doppler FFT is performedon each of the N columns of each M×N range array. In some embodiments,respective Doppler FFTs are performed in the signal processor 344 ofeach radar transceiver IC 202, 204 and the resulting range-Dopplerarrays are communicated to the processing unit 206. In some embodiments,the respective Doppler FFTs are performed by the processing unit 206.

The four range-Doppler arrays of the master radar transceiver IC 202 andthe four range-Doppler arrays of the slave radar transceiver IC 204 arethen combined 610 to generate a combined range-Doppler array. Thecombining may be performed, for example, by non-coherently adding thecorresponding elements of each of the eight range-Doppler arrays.Non-coherent addition is previously described herein. Peaks in theresulting combined range-Doppler array are potential objects and thevelocities of the potential objects are determined 612 based on thecombined range-Doppler array and the eight range-Doppler arrays. Thevelocity of an object may be determined as per the method of FIG. 7.

As shown in the flow diagram of FIG. 7, initially a velocity estimatefor the object is computed 700 based on the combined range-Dopplerarray. This velocity estimate, referred to as v_(est1) herein, may bedetermined from the location of the peak in the combined range-Dopplerarray corresponding to the object. As previously mentioned, the columnnumber of a peak in the combined range-Doppler array corresponds to thevelocity of a potential object. Note that this velocity estimate may bealiased, i.e., there may be phase rollover such that the error in theestimated velocity v_(est1) is an integer multiple of the maximummeasurable velocity v_(max).

More specifically, the relative motion of an object with respect to theradar system induces a phase change φ_(d) in the received signal acrosssubsequent chirps in a frame where the phase change is given by

$\begin{matrix}{\varnothing_{d} = \frac{4\pi \; {vT}_{c}}{\lambda}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

where v is the velocity of the object, Tc is the chirp periodicity, andλ is the wavelength corresponding to the starting frequency of a chirp.Because there is a linear progression in the phase across chirps in aframe, the phase change φ_(d) can be estimated using an FFT. Once thephase change φ_(d) is estimated, the velocity estimate v_(est1) can beestimated by inverting Eq. 1, i.e.,

$\begin{matrix}{v_{{est}\; 1} = {\frac{{\lambda\varnothing}_{d}}{4\pi \; T_{c}}.}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

Another velocity estimate is also computed 702 for the object based onphase differences of the object peak in corresponding range-Dopplerarrays. This velocity estimate, referred to as v_(est2) herein, may becomputed based on the phase differences of the object peak in therange-Doppler arrays resulting from corresponding receive channels inthe master radar transceiver IC 202 and the slave radar transceiver IC204. Correspondence of receive channels is explained below herein. Morespecifically, for each corresponding pair of receive channels, thedifference between the phase of the peak in the range-Doppler arrayresulting from the receive channel of the master radar transceiver IC202 and the phase of the peak in the range-Doppler array resulting fromthe corresponding receive channel of the slave radar transceiver IC 204is computed, e.g., one phase value is subtracted from the other. Thevelocity estimate v_(est2) may be computed as per

$\begin{matrix}{v_{{est}\; 2} = {\frac{{\Delta\varphi}\; K}{\pi}v_{\max}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

where Δφ is the average of the four phase differences, and

$v_{\max} = \frac{\lambda}{4\; T_{c}}$

where λ is the wavelength of the signal when transmission is initiated.

The derivation of Eq. 3 is as follows. Because the phase change φ_(d)can only be estimated between (−π, π), the maximum velocity v_(max) thatcan be measured is given by is given by

v_(max)=λ/(4T_(c)),  Eq. 4

which is obtained by plugging φ_(d)=π in Eq. 2. Note that Eq. 2 is trueonly if the absolute value of φ_(d)<π. In general, the phase changeφ_(d) may be aliased and hence the true velocity V_(true) is given by

$\begin{matrix}{v_{true} = {\frac{\lambda \left( {\varnothing_{d} + {2\; n\; \pi}} \right)}{4\pi \; T_{c}} = {{\frac{{\lambda\varnothing}_{d}}{4\pi \; T_{c}} + \frac{{\lambda 2}\; n}{4\; T_{c}}} = {v_{{est}\; 1} + {2\; {nv}_{\max}}}}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

by substitution from Eq. 2 and Eq. 4.

Now assume that the phase of a peak across two range-Doppler arraysdiffers by Δφ. It can be shown that

${\Delta\varnothing} = {\frac{4\pi \; v\; \Delta \; T}{\lambda}.}$

This is analogous to Eq. 1 with T_(c) replaced by ΔT. Hence, a secondestimate of the velocity v_(est2) may be computed as given by

$\begin{matrix}{v_{{est}\; 2} = {\frac{\Delta\varphi\lambda}{4{\pi\Delta}\; T} = {\frac{{\Delta\varphi}\; K}{\pi}v_{\max}}}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

using K=ΔT/T_(c) and v_(max) from Eq. 4.

The velocity of the object is then computed 704 based on the twoestimated velocities v_(est1) and v_(est2). The velocity, referred to asv_(true) herein, may be computed as per Eq. 5, i.e.,

V_(true)=v_(est1)+2nv_(max)

where n is an integer that estimates the ambiguity. The assumption isthat v_(est2) is essentially unaliased though noisy, i.e.,v_(est2)=v_(true)+noise. Comparing Eq. 5 and Eq. 6, and noting thatv_(est1) is also a noisy estimate of v_(true), the ambiguity n can beestimated as given by

n_(est)=(v_(est2)−v_(est1))/2v_(max)

where n_(est) is rounded to the nearest integer to obtain the value ofn. The value of n is applied in Eq. 5 to estimate the true velocityv_(true).

The relative placement of the transmit and receive antennas affects thephase of the signal. Thus, for the above described methods, it isimportant that the phase affects each radar transceiver IC in anidentical fashion. In some embodiments, the outputs of transmit channelsin each IC are routed to respective transmit antennas and the signalsreceived on shared receive antennas are routed to respective receivechannels on both ICs. More specifically, assume there are two transmitchannels in each radar transceiver IC. The output of one transmitchannel on the master IC and the output of one transmit channel on theslave IC are both routed to a shared single transmit antenna. Theoutputs of the other transmit channels on the two ICs are similarlyrouted to another shared single transmit channel. A transmit channel ofthe master radar transceiver IC and a transmit channel of the slaveradar transmitter IC coupled to the same transmit antenna may bereferred to as corresponding transmit channels herein.

Further, assume there are four receive channels in each radartransceiver IC. One receive channel on the master IC and one receivechannel on the slave IC are coupled to a shared single receive antennato receive signals. The other receive channels on the ICs are similarlypaired and coupled to respective shared receive antennas to receivesignals. A receive channel of the master radar transceiver IC and areceive channel of the slave radar transmitter IC coupled to the samereceive antenna may be referred to as corresponding receive channelsherein.

FIG. 8 is a simple example illustrating the above antenna routingbetween two radar transceiver ICs 800, 802, each having one transmitchannel and four receive channels. The transmit channel on the radartransceiver IC 800 and the transmit channel on the radar transceiver IC802 are coupled to the single shared transmit antenna 804. Forsimplicity, the coupling to only one receive antenna 806 is shown. Areceive channel in the IC 800 and a receive channel in the IC 802 arecoupled to the shared receive antenna 806. The other receive antennasare similarly coupled to respective receive channels in the IC 800 andthe IC 802.

The interconnection of the antennas as described requires combining thesignals from transmit channels of multiple radar transceiver ICs to thesame transmit antenna and splitting the signals from the receiveantennas to receive channels of multiple ICs. Placing suchsplitters/combiners at high frequency, e.g., 77 GHz, can result inlosses. The use of splitters and combiners can be avoided by having eachIC use a different set of antennas. However, in such an arrangement,ensuring that the phase relationships between corresponding transmit andreceive antennas remain the same across ICs is important. In someembodiments, this is achieved using the principle of antennaequivalence.

A transmit/receive (TX-RX) antenna pair is defined by the total distancetraversed by the RF signal from the transmit antenna to the object andback from the object to the receive antenna. Thus, any two TX-RX antennapairs are equivalent as long as the distance TX->object->RX is the samefor both. Consider the TX-RX antenna pairs A′-B′ and A-B shown in FIG.9. Rays emanating from the TX antennas A and A′ toward an object locatedat an angle θ are depicted. In addition, reflected rays from the objectreceived by the RX antennas B and B′ are shown. The distance of theobject from the TX and RX antennas is assumed to be much larger than theinter-antenna distances thus making the rays from A and A′ and to B andB′ parallel.

The TX antenna A′ is at a distance d to the left of the TX antenna A.Thus, the TX antenna A′ is closer to the object by an amount dsin(θ).Similarly, the RX antenna B′ is at a distance of d to the right of theRX antenna B. Thus, the RX antenna B′ is farther from the object by anamount dsin(θ). The total distance from A->object->B is the same as thetotal distance from A′->object->B′, thus the antenna pairs A-B and A′-B′are equivalent. More generally, two TX-RX antenna pairs are equivalentas long as the mid-points of the line connecting each of the TX-RX pairsare the same. The receive channels coupled to the receive antennas inequivalent TX-RX antenna pairs may be referred to as correspondingreceive channels herein.

FIG. 10 shows an example antenna configuration designed using theprinciple of antenna equivalence. In this example, one radar transceiverIC (not shown) is coupled to four receive antennas referred tocollectively as RX1 and a single transmit antenna TX1. Another radartransceiver IC (not shown) is also coupled to four receive antennasreferred to collectively as RX2 and a single transmit antenna TX2. TX1and RX1 and TX2 and RX2 are connected to TX/RX channels of therespective ICs. In this example, the distance between TX1 and TX2 isfour times the equivalent distances between consecutive RX antennas inRX1 and RX2. Thus, the TX1->RX1 antenna a pair is equivalent to TX2->RX2antenna a pair, the TX1->RX1 antenna b pair is equivalent to TX2->RX2antenna b pair, etc. The principle of antenna equivalence ensures thatsuch a configuration has the same behavior as the example configurationof FIG. 8.

In some embodiments, a common antenna-array architecture operable in twomodes is used. One mode favors a higher angle resolution and the otherfavors a higher maximum measurable velocity. An example embodiment isexplained in reference to the example of FIG. 10. When higher angleresolution is preferred, only one transmit antenna is operational, e.g.,TX1, and the associated transmit channel is operational while TX2 andthe associated transmit channel are not used. When a frame of chirps istransmitted by TX1, the reflected chirps are received by all eightreceive antennas of RX1 and RX2. Compared to a radar system with asingle radar transceiver IC, this configuration may provide up to a 2Ximprovement in angle resolution. However, the maximum measurablevelocity is identical to that of a radar system with a single radartransceiver IC.

When a higher maximum measurable velocity is preferred, both TX1 and TX2transmit frames of chirps in accordance with a method described herein.The reflected chirps from the TX1 transmission are received in the RX1antennas and the reflected chirps from the TX2 transmission are receivedin the RX2 antennas. Note that the staggered timing of the chirptransmission guarantees non-interference. That is, each IC independentlyprocesses the reflected chirps from the frames transmitted by the ICwithout any interference from signals from the other IC. The frequencyof the IF signal depends on the delay between the TX and RX signals. Asmall separation in time in the transmitted signals of the two ICsensures that any signals from the one IC received in the RX channels ofthe other IC will generate an IF signal that is outside the IF bandwidthof the other IC, thus ensuring non-interference. The signals areprocessed as per the method to achieve a higher maximum measurablevelocity. In this mode of operation, the maximum measurable velocity isincreased by a factor of K as previously described herein as compared toa radar system with a single radar transceiver IC. However, the angleresolution will be the same as that of a radar system with a singleradar transceiver IC.

Any suitable technique for mode switching may be used, e.g., switchingthe mode for each frame of chirps. The implementation of the switchinglogic may be performed, for example, by the external processor of theradar system.

Routing mismatches, e.g., differences in the lengths of the connectionsfrom the antennas to the radar transceiver ICs, and parametricvariations between ICs may cause systematic phase offsets betweencorresponding receive channels in the two ICs. In some embodiments,calibration is performed based on stationary objects in the scene todetermine the phase offsets. For stationary objects, there should be nophase change across chirps in the absence of a systematic phase offset.

An initial calibration to determine the systematic phase offsets may beperformed, e.g., in a factory, using a known stationary object. FIG. 11is a flow diagram of a method for determining the systematic phaseoffsets using a known stationary object that may be performed in a radarsystem such as that of FIGS. 2 and 3. The method may be performed whenthe radar system is operated in a calibration mode. The method isexplained assuming that each radar transceiver IC has four receivechannels and two transmit channels. One of ordinary skill in the artwill understand embodiments in which the radar transceiver ICs may havemore or fewer receive channels and/or transmit channels.

The calibration process begins with the transmission of a frame ofchirps initiated 1100 by the master radar transceiver IC 202. Thetransmission of a frame of chirps by the slave radar transceiver IC 204is then initiated 1102 with a time delay of ΔT. Any suitable value of ΔTmay be used that does not cause interference between the ICs 202, 204,and minimizes error in the calculation of the systematic phase offsets.In general, a suitable value may be on the order of a few microseconds,e.g., between 10 and 100 us. Digital IF signals are generated 1104 ineach receive channel 202 of each of the radar transceiver ICs 202, 204as the reflected chirps from the object are received. Thus, four digitalIF signals, one from each receive channel 202, are generated in eachradar transceiver IC 202, 204.

Range FFTs are performed 1106 on the digital IF signals to generate arange array for each digital IF signal. Doppler FFTs are then performed1108 on each of the range arrays to generate eight range-Doppler arrays.For each corresponding pair of receive channels, the difference betweenthe phase of the object peak in the range-Doppler array resulting fromthe receive channel of the master radar transceiver IC 202 and the phaseof the object peak in the range-Doppler array resulting from thecorresponding receive channel of the slave radar transceiver IC 204 iscomputed 1110, e.g., one phase value is subtracted from the other. Asearch in each of the range-Doppler arrays may need to be performed tolocate the object peak. Because the stationary object is known, theapproximate location of a peak or peaks corresponding to the object maybe known. Thus, the search can performed in the approximate area of eachof the range-Doppler arrays to locate the peak. Further, if the objectis large, there may be many peaks corresponding to the object. If thereare multiple peaks, any of the peaks may be used.

The computed phase difference for a corresponding pair of receivechannels is the systematic phase offset for the receive channel pair.The four systematic phase offsets are stored 1112 for use in thevelocity computations performed during normal operation of the radarsystem 200.

As part of the velocity computation for an object, the systematic phaseoffsets may be used in the computation of v_(est2) as described inreference to the method of FIG. 7. More specifically, in step 702, thesystematic phase offset for a receive channel pair is subtracted fromthe phase difference computed for the receive channel pair prior tocomputing the average of the four phase differences. The systematicphase offsets may also be used as part of the velocity computation foran object as described in reference to the method of FIG. 4. Morespecifically, the systematic phase offsets may be applied tocorresponding range arrays generated in step 406 prior to interleavingthe range arrays in step 408.

In some embodiments, calibration may also be performed to update thesystematic phase offsets while the radar system 200 is operational if astationary object can be identified in the FOV of the radar. FIG. 12 isa flow diagram of a method for determining the systematic phase offsetsusing an identified stationary object that may be performed in a radarsystem such as that of FIGS. 2 and 3. The method may be performed whenthe radar system is operated in a calibration mode. Further, the methodmay be performed periodically, on command, and/or when the radar systemis initialized. The method is explained assuming that each radartransceiver IC has four receive channels and two transmit channels. Oneof ordinary skill in the art will understand embodiments in which theradar transceiver ICs may have more or fewer receive channels and/ortransmit channels.

The calibration process begins with the transmission of a frame ofchirps initiated 1200 by the master radar transceiver IC 202. Thetransmission of a frame of chirps by the slave radar transceiver IC 204is then initiated 1201 with a time delay of ΔT₁. Any suitable value ofΔT₁ may be used. Suitable values for time delays used during calibrationare previously described in reference to FIG. 11. Digital IF signals aregenerated 1202 in each receive channel 202 of each of the radartransceiver ICs 202, 204 as the reflected chirps are received. Thus,four digital IF signals, one from each receive channel 202, aregenerated in each radar transceiver IC 202, 204.

Range-Doppler arrays are then computed 1204 for each receive channel.When the range-Doppler arrays are available, phase differences of objectpeaks are computed 1206. That is, for each corresponding pair of receivechannels, the difference between the phase of an object peak in therange-Doppler array resulting from the receive channel of the masterradar transceiver IC 202 and the phase of the object peak in therange-Doppler array resulting from the corresponding receive channel ofthe slave radar transceiver IC 204 is computed, e.g., one phase value issubtracted from the other. Thus, four phase differences are computed foreach object peak.

The transmission of a frame of chirps is then initiated 1208 by themaster radar transceiver IC 202. The transmission of a frame of chirpsby the slave radar transceiver IC 204 is also initiated 1209 with a timedelay of ΔT₂. Any suitable value of ΔT₂ may be used with the caveat thatif the values of ΔT₁ and ΔT₂ are too close, the determination of whetheror not an object is stationary may be prone to error. Examples ofsuitable values of ΔT₁ and ΔT₂ are 20 us and 40 us, respectively.Digital IF signals are generated 1210 in each receive channel 202 ofeach of the radar transceiver ICs 202, 204 as the reflected chirps arereceived. Thus, four digital IF signals, one from each receive channel202, are generated in each radar transceiver IC 202, 204.

Range-Doppler arrays are then computed 1212 for each receive channel.When the range-Doppler arrays are available, phase differences of objectpeaks are computed 1214. That is, for each corresponding pair of receivechannels, the difference between the phase of a object peak in therange-Doppler array resulting from the receive channel of the masterradar transceiver IC 202 and the phase of the object peak in therange-Doppler array resulting from the corresponding receive channel ofthe slave radar transceiver IC 204 is computed, e.g., one phase value issubtracted from the other. Thus, four phase differences are computed foreach object peak.

A determination 1216 is then made as to whether or not a stationaryobject is present in the scene based on the two sets of object peakphase differences. That is, for an object peak appearing in both of therange-Doppler arrays, the difference between each phase difference ofthe four phase differences determined for the peak using time delay ΔT₁and the respective phase difference of the four phase differencesdetermined for the peak using time delay ΔT₂ is compared to a thresholddetermined by the signal-to-noise ratio. If each of the four differencesis less than the threshold, then the peak corresponds to a stationaryobject. Object peaks may be searched until a peak corresponding to astationary object is found or all object peaks have been considered. Ifno stationary object is present 1216, the method terminates.

If a peak corresponding to a stationary object is found 1216, then thesystematic phase offsets are computed based on the four phasedifferences determined for the peak using time delay ΔT₁ and the fourphase differences determined for the peak using time delay ΔT₂. Morespecifically, corresponding phase differences are averaged to determinethe four systematic phase offsets, one for each corresponding pair ofreceive channels. The four systematic phase offsets are stored for usein the velocity computations performed during normal operation of theradar system 200. Use of the systematic phase offsets in the method ofFIG. 7 and the method of FIG. 4 is previously described herein.

In some embodiments, if multiple object peaks correspond to thestationary object, systematic phase offsets are also determined forthese peaks. In such embodiments, the final four systematic phaseoffsets are determined by averaging corresponding systematic phaseoffsets of all the peaks.

Other Embodiments

While the disclosure has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the disclosure as disclosed herein.

For example, embodiments have been described herein in a radar systemincludes two radar transceiver ICs. One of ordinary skill in the artwill understand embodiments using symmetric staggering in which a radarsystem includes more than two transceiver ICs. In general, if there areN radar transceiver ICs in a radar system, the transmission of a frameof chirps from each transceiver IC is staggered by Tc/N from theprevious one, thus ensuring that the transmitted chirps are equispacedwith respect to the chirps of the immediate neighboring ICs.

In another example, embodiments have been described herein assuming Ntime samples in a chirp and that N range results each corresponding to aspecific range bin are stored for the chirp. One of ordinary skill inthe art will understand embodiments in which a range FFT is performed onN time samples in a chirp to create N₁>N range results using forexample, a zero padded FFT. Similarly, one of ordinary skill in the artwill understand that a Doppler FFT may be performed over M range binscorresponding to M frames to create M₁>M range-Doppler results.

In another example, embodiments have been described herein in which theradar transceiver ICs in the front end of the radar system have a masterslave relationship. One of ordinary skill in the art will understandembodiments in which the radar transceiver ICs do not have a masterslave relationship, e.g., an external PLL is used to provide signals toall of the transceiver ICs.

In another example, embodiments employing the idea of antennaequivalence have been describe herein assuming one transmit antenna perradar transceiver IC. One of ordinary skill in the art will understandembodiments in which more than one transmit antenna is used. One ofordinary skill in the art will also understand embodiments having moreor fewer receive antennas.

In another example, embodiments have been described herein in whichspecific parts of the radar signal processing are performed in the radartransceiver ICs and the remaining signal processing is performed by aprocessing unit receiving results from the radar transceiver ICs. One ofordinary skill in the art will understand embodiments in which thedistribution of the signal processing between the radar transceiver ICsand the processing unit differs from the examples described herein.

Although method steps may be presented and described herein in asequential fashion, one or more of the steps shown in the figures anddescribed herein may be performed concurrently, may be combined, and/ormay be performed in a different order than the order shown in thefigures and/or described herein. Accordingly, embodiments should not beconsidered limited to the specific ordering of steps shown in thefigures and/or described herein.

Certain terms are used throughout the description and the claims torefer to particular system components. As one skilled in the art willappreciate, components in radar systems may be referred to by differentnames and/or may be combined in ways not shown herein without departingfrom the described functionality. This document does not intend todistinguish between components that differ in name but not function. Inthe following discussion and in the claims, the terms “including” and“comprising” are used in an open-ended fashion, and thus should beinterpreted to mean “including, but not limited to . . .” Also, the term“couple” and derivatives thereof are intended to mean an indirect,direct, optical, and/or wireless electrical connection. Thus, if a firstdevice couples to a second device, that connection may be through adirect electrical connection, through an indirect electrical connectionvia other devices and connections, through an optical electricalconnection, and/or through a wireless electrical connection, forexample.

It is therefore contemplated that the appended claims will cover anysuch modifications of the embodiments as fall within the true scope ofthe disclosure.

What is claimed is:
 1. A radar system having a maximum measurable velocity v_(max), the radar system comprising: a first radar transceiver integrated circuit (IC) configurable to transmit a first frame of chirps; and a second radar transceiver IC configurable to transmit a second frame of chirps at a time delay AT from when the first radar transceiver IC begins transmitting the first frame of chirps, wherein ΔT=T_(c)/K, K≥2 and T_(c) is an elapsed time from a start of one chirp in the first frame of chirps and the second frame of chirps and a start of a next chirp in the first frame and the second frame, wherein the radar system is configured to determine a velocity of an object in a field of view (FOV) of the radar system based on first digital intermediate frequency (IF) signals generated by the first radar transceiver IC responsive to receiving reflected chirps of the first frame of chirps and second digital IF signals generated by the second radar transceiver IC responsive to receiving reflected chirps of the time delayed second frame of chirps, wherein v_(max) is increased by a factor of K.
 2. The radar system of claim 1, wherein K=2 and the radar system is further configured to: perform range fast Fourier transforms (FFTs) on each digital IF signal to generate a range array for each digital IF signal; interleave corresponding range arrays of the first digital IF signals and the second digital IF signals to generate interleaved range arrays; perform Doppler FFTs on each interleaved range array to generate a range-Doppler array for each range array; and combine the range-Doppler arrays to form a combined range-Doppler array, wherein the radar system is configured to determine the velocity of the object using the combined range-Doppler array.
 3. The radar system of claim 1, wherein K>2 and the radar system is further configured to: perform range fast Fourier transforms (FFTs) on each digital IF signal to generate a range array for each digital IF signal; perform Doppler FFTs on each range array to generate a range-Doppler array for each digital IF signal; and combine the range-Doppler arrays to generate a combined range-Doppler array, wherein the radar system is configured to determine the velocity of the object based on the combined range-Doppler array and the range-Doppler arrays.
 4. The radar system of claim 3, wherein to determine the velocity of an object, the radar system is further configured to: compute a first velocity estimate for the object based on the combined range-Doppler array; compute a second velocity estimate for the object based on phase differences of a peak corresponding to the object in corresponding range-Doppler arrays of the first digital IF signals and the second digital IF signals; and compute the velocity of the object based on the first velocity estimate and the second velocity estimate.
 5. The radar system of claim 4, wherein the radar system is further configured to: compute the first velocity estimate v_(est1) from a peak corresponding to the object in the combined range-Doppler array; compute the second velocity estimate v_(est2) as per ${v_{{est}\; 2} = {\frac{{\Delta\varphi}\; K}{\pi}v_{\max}}},$ wherein Δφ is an average of the phase differences; and compute the velocity v_(true) of the object as per v_(true)=v_(est1)+2nv_(max), wherein n is determined as per n_(est)=(v_(est2)−v_(est1))/2v_(max), wherein n is n_(est) rounded to a nearest integer.
 6. The radar system of claim 1, wherein the radar system is configured to switch between two modes, a mode that favors higher angle resolution and a mode that favors higher maximum measurable velocity.
 7. The radar system of claim 1, wherein the first radar transceiver IC is coupled to a first transmit antenna and a first receive antenna and the second radar transceiver IC is coupled to a second transmit antenna and a second receive antenna, wherein a midpoint of the first transmit antenna and the first receive antenna coincides with a midpoint of the second transmit antenna and the second receive antenna.
 8. The radar system of claim 1, wherein the radar system is further configured to operate in a calibration mode to determine systematic phase offsets between corresponding receive channels of the first radar transceiver IC and the second radar transceiver IC, wherein the systematic phase offsets are used in determining the velocity of the object.
 9. The radar system of claim 8, wherein to determine a systematic phase offset, the radar system is further configured to find a first peak corresponding to a known stationary object in a first range-Doppler array generated responsive to receiving first reflected chirps of a first test frame of chirps in a first receive channel of the first radar transceiver IC; find a second peak corresponding to the first peak in a second range-Doppler array generated responsive to receiving second reflected chirps of a second test frame of chirps in a receive channel corresponding to the first receive channel of the second radar transceiver IC, the second test frame transmitted at a time delay from transmission of the first frame; and determine the systematic phase offset based on a difference between a phase at the first peak and a phase at the second peak.
 10. The radar system of claim 8 wherein to determine a systematic phase offset, the radar system is further configured to identify a stationary object in a field of view of the radar system, wherein to identify the stationary object, the radar system is configured to: find a first peak corresponding to an object in a first range-Doppler array generated responsive to receiving first reflected chirps of a first test frame of chirps in a first receive channel of the first radar transceiver IC; find a second peak corresponding to the first peak in a second range-Doppler array generated responsive to receiving second reflected chirps of a second test frame of chirps in a receive channel corresponding to the first receive channel of the second radar transceiver IC, the second test frame transmitted at a first time delay from transmission of the first test frame; find a third peak corresponding to the object in a third range-Doppler array generated responsive to receiving third reflected chirps of a third test frame of chirps in the first receive channel of the first radar transceiver IC; find a fourth peak corresponding to the third peak in a fourth range-Doppler array generated responsive to receiving fourth reflected chirps of a fourth test frame of chirps in the receive channel corresponding to the first receive channel of the second radar transceiver IC, the fourth test frame transmitted at a second time delay from transmission of the third test frame; and determine that the object is stationary when a first phase difference at the first peak and the second peak is sufficiently similar to a second phase difference at the third peak and the fourth peak; and determine the systematic phase offset based on the first phase difference and the second phase difference.
 11. A method for determining velocity of objects in a radar system having a maximum measurable velocity v_(max), the method comprising: initiating transmission of a first frame of chirps by a first radar transceiver integrated circuit (IC) in the radar system; initiating transmission of a second frame of chirps by a second radar transceiver IC in the radar system at a time delay ΔT from when the first radar transceiver IC begins transmitting the frame of chirps, wherein ΔT=T_(c)/K, K≥2 and T_(c) is an elapsed time from a start of one chirp in the first frame of chirps and the second frame and a start of a next chirp in the first frame and the second frame; generating first digital intermediate frequency (IF) signals by the first radar transceiver IC responsive to receiving reflected chirps of the first frame of chirps; generating second digital IF signals by the second radar transceiver IC responsive to receiving reflected chirps of the time delayed second frame of chirps; and determining a velocity of an object in a field of view (FOV) of the radar system based on the first digital IF signals and the second digital IF signals, wherein v_(max) is increased by a factor of K.
 12. The method of claim 11, wherein K=2 and the method further comprises: performing range fast Fourier transforms (FFTs) on each digital IF signal to generate a range array for each digital IF signal; interleaving corresponding range arrays of the first digital IF signals and the second digital IF signals to generate interleaved range arrays; performing Doppler FFTs on each interleaved range array to generate a range-Doppler array for each range array; and combining the range-Doppler arrays to form a combined range-Doppler array; and determining the velocity of the object using the combined range-Doppler array.
 13. The method of claim 11, wherein K>2 and the method further comprises: performing range fast Fourier transforms (FFTs) on each digital IF signal to generate a range array for each digital IF signal; performing Doppler FFTs on each range array to generate a range-Doppler array for each digital IF signal; and combining the range-Doppler arrays to generate a combined range-Doppler array; and determining the velocity of the object based on the combined range-Doppler array and the range-Doppler arrays.
 14. The method of claim 13, wherein determining the velocity further comprises: computing a first velocity estimate for the object based on the combined range-Doppler array; computing a second velocity estimate for the object based on phase differences of a peak corresponding to the object in corresponding range-Doppler arrays of the first digital IF signals and the second digital IF signals; and computing the velocity of the object based on the first velocity estimate and the second velocity estimate.
 15. The method of claim 14, wherein computing a first velocity estimate further comprises computing the first velocity estimate v_(est1) from a peak corresponding to the object in the combined range-Doppler array; computing a second velocity estimate further comprises computing the second velocity estimate v_(est2) as per ${v_{{est}\; 2} = {\frac{{\Delta\varphi}\; K}{\pi}v_{\max}}},$ wherein Δφ is an average of the phase differences; and computing the velocity further comprises computing the velocity v_(true) of the object as per v_(true)=v_(est1)+2nv_(max), wherein n is determined as per n_(est)=(v_(est2)−v_(est1))/2v_(max), wherein n is n_(est) rounded to a nearest integer.
 16. The method of claim 11, wherein the first radar transceiver IC is coupled to a first transmit antenna and a first receive antenna and the second radar transceiver IC is coupled to a second transmit antenna and a second receive antenna, wherein a midpoint of the first transmit antenna and the first receive antenna coincides with a midpoint of the second transmit antenna and the second receive antenna.
 17. The method of claim 11, wherein the radar system is configured to switch between two modes, a mode that favors higher angle resolution and a mode that favors higher maximum measurable velocity.
 18. The method of claim 11, wherein determining a velocity further comprises using systematic phase offsets between corresponding receive channels of the first radar transceiver IC and the second radar transceiver IC in determining the velocity of the object.
 19. The method of claim 18, wherein the radar system determines a systematic phase offset when operated in a calibration mode by: finding a first peak corresponding to a known stationary object in a first range-Doppler array generated responsive to receiving first reflected chirps of a first test frame of chirps in a first receive channel of the first radar transceiver IC; finding a second peak corresponding to the first peak in a second range-Doppler array generated responsive to receiving second reflected chirps of a second test frame of chirps in a receive channel corresponding to the first receive channel of the second radar transceiver IC, the second test frame transmitted at a time delay from transmission of the first frame; and determining the systematic phase offset based on a difference between a phase at the first peak and a phase at the second peak.
 20. The method of claim 18, wherein the radar system determines a systematic phase offset when operated in a calibration mode by: identifying a stationary object in a field of view of the radar system by: finding a first peak corresponding to an object in a first range-Doppler array generated responsive to receiving first reflected chirps of a first test frame of chirps in a first receive channel of the first radar transceiver IC; finding a second peak corresponding to the first peak in a second range-Doppler array generated responsive to receiving second reflected chirps of a second test frame of chirps in a receive channel corresponding to the first receive channel of the second radar transceiver IC, the second test frame transmitted at a first time delay from transmission of the first test frame; finding a third peak corresponding to the object in a third range-Doppler array generated responsive to receiving third reflected chirps of a third test frame of chirps in the first receive channel of the first radar transceiver IC; finding a fourth peak corresponding to the third peak in a fourth range-Doppler array generated responsive to receiving fourth reflected chirps of a fourth test frame of chirps in the receive channel corresponding to the first receive channel of the second radar transceiver IC, the fourth test frame transmitted at a second time delay from transmission of the third test frame; and determining that the object is stationary when a first phase difference at the first peak and the second peak is sufficiently similar to a second phase difference at the third peak and the fourth peak; and determining the systematic phase offset based on the first phase difference and the second phase difference. 